Yes, you can, but you may get errors, if your HD is not properly supported by the USB drivers on the Pi. It has been reported that Broadcom is not supported.
The procedure I followed was to install Rasbian OS onto a 4gig USB stick using “Berryboot”. Then on Windows, I used EASUS partition master to copy the Linux partition from the USB stick to the USB hard drive.
Then I unplugged the USB Stick from the Pi, and inserted the USB connector to the USB Hard Drive. This booted up okay, but I got an error trying to run Midori. The other browser, Dillo, worked okay though.
There is a slight speed advantage, but the principal advantage would be having a larger amount of storage space than there would be on a USB stick, but that is if you don’t get any errors!